Diffraction of light question - How do I approach this?

[Micky76]

Homework Statement

Question:
Blue light of wavelength 485.6nm from a star is incident normally on a diffraction grating. The light is diffracted into a number of beams, as shown in Fig 5.4.(attached)

The angular separation of the two second-order beams is 45.72 degrees.
Calculate the number of lines per millimetre on the grating.

Homework Equations

The Attempt at a Solution

I genuinely do not know where to start the question. I know the formula for Young's double slit experiment however this does not seem to relate to it at all. Any suggestions for starting the question would be really appreciated.

 

[vela]

Read your textbook. It surely mentions diffraction gratings.

 

[Micky76]

Never seen the formula before. The question is from an old past paper so it might be off the specification. The only thing relating to path difference that I have seen is the Young's modulus experiment. Anyways I had an attempt, is my working correct?

Θ = 45.72/2 = 22.86 degrees
2*485.6*10^-9 = d sin(22.86)
d = 2.50*10^-6 m
d = 2.50*10^-3 mm
N = 1/d = 1/(2.50*10^-3) = 400
Lines per mm = 400

There is no mark scheme for this so if someone could verify my working that would be great.

 

[vela]

Looks good. With a diffraction grating the only difference is the maxima become sharper otherwise it's the same as the two-slit experiment

 

[Nickie]

As a scientist, it is important to approach this question systematically and logically. The first step would be to understand the concept of diffraction and how it relates to the diffraction grating. Diffraction is the bending of light as it passes through an aperture or around an obstacle. A diffraction grating is a device with a series of closely spaced parallel lines or slits that diffract light into multiple beams.

Next, we can use the given information to solve the problem. The angular separation of the second-order beams can be calculated using the formula:
sinθ = mλ/d, where θ is the angle of diffraction, m is the order of the diffraction (in this case, m=2), λ is the wavelength of the light, and d is the distance between the lines on the grating.

We know the value of θ (45.72 degrees) and λ (485.6nm), so we can rearrange the formula to solve for d:
d = mλ/sinθ

Substituting the values, we get:
d = (2)(485.6nm)/(sin 45.72 degrees) = 1381.07nm

Now, we need to convert the distance between lines (d) into lines per millimeter. This can be done by taking the reciprocal of d and then converting the units:
Number of lines per millimeter = 1/(d/1000) = 1/(1381.07nm/1000) = 724.64 lines/mm

Therefore, the number of lines per millimeter on the grating is approximately 724.64 lines/mm.

In summary, to approach this question, we need to understand the concept of diffraction and use the given information to apply the relevant formula. It is also important to carefully convert units and double check our calculations to ensure accuracy.